139-բ,դ,զ,ը. Լուծեք անհավասարումը․
բ) 0,5x2 > x
0,5x2 – x > 0
0,5x2 – x = 0
a = 0,5
b = -1
c = 0
D = b2 – 4ac = 1 – 4 * 0,5 * 0 = 1
x = -b ± √D/2a = 1 ± 1/2 * 0,5 = 1 ± 1
x1 = 1 + 1 = 2
x2 = 1 – 1 = 0
0,5x2 – x > 0
x ∈ (-∞; 0) ∪ (2; +∞)
դ) 7/8x > 13/5x2
-13/5x2 + 7/8x > 0
-1 3/5x2 + 7/8x = 0
a = -1 3/5 = 8/5
b = 7/8
c = 0
D = b2 – 4ac = 49/64 – 4 * 8/5 * 0 = 49/64
x = -b ± √D/2a = –7/8 ± √49/64/2 * 8/5 = –7/8 ± 7/8/16/5 = 5(-35/8 ± 35/8)/16 = –35/8 ± 35/8/16
x1 = –35/8 + 35/8/16 = 35/8/8 = 35/64
x2 = –35/8 – 35/8/16 = 0
-13/5x2 + 7/8x > 0
x ∈ (-∞; 0) ∪ (35/64; +∞)
զ) 5 < -x2
x2 + 5 < 0
x2 + 5 = 0
a = 1
b = 0
c = 5
D = b2 – 4ac = 0 – 4 * 1 * 5 = -20
D < 0
x2 + 5 < 0
x ∈ ∅
ը) 3x2 > -5
3x2 + 5 > 0
a = 3
b = 0
c = 5
D = b2 – 4ac = 0 – 4 * 3 * 5 = -60
D < 0
3x2 + 5 > 0
x ∈ (-∞; +∞)
140-բ,դ. Լուծեք անհավասարումը․
բ) 12x2 > 8x + 3
12x2 – 8x – 3 > 0
12x2 – 8x – 3 = 0
a = 12
b = -8
c = -3
D = b2 – 4ac = 64 – 4 * 12 * -3 = 208
x = -b ± √D/2a = 8 ± √208/2 * 12 = 8 ± 4√13/24 = 2 ± √13/6
x1 = 2 + √13/6
x2 = 2 – √13/6
12x2 – 8x – 3 > 0
x ∈ (-∞; 2 – √13/6) ∪ (2 + √13/6; +∞)
դ) 7x2 – 6 > 25x
7x2 – 25x – 6 > 0
7x2 – 25x – 6 = 0
a = 7
b = -25
c = -6
D = b2 – 4ac = 625 – 4 * 7 * -6 = 625 + 168 = 793
x = -b ± √D/2a = 25 ± √793/2 * 7 = 25 ± √793/14
x1 = 25 + √793/14
x2 = 25 = √793/14
7x2 – 25x – 6 > 0
x ∈ (-∞; 25 = √793/14) ∪ (25 + √793/14; +∞)
141-բ,դ. Լուծեք անհավասարումը․
բ) 2(x + 1)2 < 2(2x + 1) – (x – 1)(x + 1)
2(x2 + 2x + 1) < 4x + 2 – x2 + 1
2x2 + 4x + 2 < -x2 + 4x + 3
-3x2 + 1 > 0
-3x2 + 1 > 0
a = -3
b = 0
c = 1
D = b2 – 4ac = 0 – 4 * -3 * 1 = 12
x = -b ± √D/2a = ±√12/2 * -3 = ±12/-6 = ±2
x1 = 2
x2 = -2
-3x2 + 1 > 0
x ∈ (-∞; -2) ∪ (2; +∞)
դ) (x + 3)(x – 2) > 3x + 10 – (x + 2)2
x2 – 2x + 3x – 6 > 3x + 10 – x2 + 4x + 4
x2 + x – 6 > -x2 + 7x + 14
2x2 – 6x – 20 > 0
2x2 – 6x – 20 = 0
a = 2
b = -6
c = -20
D = b2 – 4ac = (-6)2 – 4 * 2 * -20 = 36 + 160 = 196
x = -b ± √D/2a = 6 ± √196/2 * 2 = 6 ± 14/4 = 1,5 ± 3,5
x1 = 1,5 + 3,5 = 5
x2 = 1,5 – 3,5 = -2
2x2 – 6x – 20 > 0
x ∈ (-∞; -2) ∪ (5; +∞)
143-բ,դ. Լուծեք անհավասարումը․
բ) x2 – 7 – 2x/4 > 0,2
x2 – 1,75 – 0,5x > 0,2
x2 – 0,5x – 1,95 > 0
x2 – 0,5x – 1,95 > 0
a = 1
b = -0,5
c = -1,95
D = b2 – 4ac = (-0,5)2 – 4 * 1 * -1,95 = 0,25 + 7,8 = 8,05
x = -b ± √D/2a = 0,5 ± √8,05/2
x1 = 0,5 + √8,05/2
x2 = 0,5 – √8,05/2
2x2 – 6x – 20 > 0
x ∈ (-∞; 0,5 – √8,05/2) ∪ (0,5 + √8,05/2; +∞)
դ) 12 – x2/4 – x/3 > (x – 3)2/12
3 – 0,25x2 – 1/3x > x2 – 6x + 9/12
–3/12x2 – 4/12x + 36/12 > 1/12x2 – 6/12x + 9/12
–4/12x2 + 2/12x + 9/4 > 0
–1/3x2 + 1/6x + 9/4 > 0
–1/3x2 + 1/6x + 9/4 = 0
a = –1/3
b = 1/6
c = 9/4
D = b2 – 4ac = (1/6)2 – 4 * –1/3 * 9/4 = 1/36 + 108/36 = 109/36
x = -b ± √D/2a = –1/6 ± √109/36/2 * –1/3 = –1/6 ± √109/36/–2/3 = 3/6 ± 3√109/36/2 = 1,5/6 ± 1,5√109/36 = 1/4 ± 1,5√109/36
x1 = 1/4 + 1,5√109/36
x2 = 1/4 – 1,5√109/36
2x2 – 6x – 20 >
x ∈ (-∞; 1/4 – 1,5√109/36) ∪ (1/4 + 1,5√109/36; +∞)
144-բ,դ. Գտեք ֆունկցիայի որոշման տիրույթը․
բ) y = 1/√(x – 1)
√(x – 1) > 0
x – 1 > 0
x > 1
D(f) = (1; +∞)
դ) y = 4/√x2
y = 4/x
x ≠ 0
x ∈ (-∞; 0) ∪ (0; +∞)
Դավիթ Ապիտոնյան 